Allowance for Specular Reflection

A simple engineering approach to specular reflection is the so-called diffuse plus specular reflection model. Here the total reflectivity p2 = 1 — e = ps + pa is represented as the sum of a diffuse component 

For the case of (infinite) parallel flat plates where A = A2, Eq. (5-134) leads to a general formula similar to Eq. (5-134 ) but with the stipulation here that 8i = 1 - pD1 - psi and e2 = 1 - pD2 ps2- 

Another particularly interesting limit of Eq. (5-134) occurs when A2 Ai, which might represent a small sphere irradiated by an infinite surroundings which can reflect radiation originating at Ab back to Ai. That is to say, even though A2 — , the self total exchange area does not necessarily vanish, to wit 

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Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Specular reflection IR spectroscopy has been used by Cole and coworkers to study the orientation and structure in PET films [36,37]. It has allowed characterizing directly very highly absorbing bands in thick samples, in particular the carbonyl band that can show saturation in transmission spectra for thickness as low as 2 pm. The orientation of different conformers could be determined independently. Specular reflection is normally limited to uniaxial samples because the near-normal incident light does not allow measuring Ay. However, it was shown that the orientation parameter along the ND can be indirectly determined for PET by using the ratio of specifically selected bands [38]. This approach was applied to the study of biaxially oriented PET bottles [39]. 

Figure 10.17 Devices allowing the study of samples by reflection, (a) Schematic representation of two ATR devices (attenuated total reflection) a model with a trapezium crystal for multiple reflections and a model for single reflection with solid microsamples (the application of a weight improves the contact of the sample with the crystal s rounded form). Basic formula and notion of critical angle (h) Specular reflection device. Optical pathway of the apparatus at a fixed angle of 30 ° for highly reflecting samples and of 60 ° for the contrary (c) Optical scheme for a diffuse reflection device and diagram of a Spectra Tech model.

Both Carr and Brice, Halwer and Speiser have studied carefully the calibration of absolute intensity of scattering by comparison with the reflected intensity from diffusely reflecting surfaces, such as magnesium oxide or casein paint. Apparently none of these surfaces acts as an ideal diffuse reflector there is always at least a small fraction of the light which undergoes specular reflection, and this must be allowed for in the calibration of light scattering measurements. 

Scratch hardness is particularly important in plastics used for their optical properties and is usually determined by some of mar-resistance test. In one type of test a specimen is subjected to an abrasive treatment by allowing exposure to a controlled stream of abrasive, and its gloss (specular reflection) is measured before and after the treatment. In some tests the light transmission property of the plastic is measured before and after marring. 

A reference beam is used with a plate of BaS04 as the reference standard. Thus, all measurements are relative and are compared to the reflection from a barium sulfate standard. Because the specular reflection from a pearlescent pigment is so much greater than the reflection from a barium sulfate plate, a neutral density filter allowing only 10% of the light to pass was placed in the beam incident on the sample for measurements made at -15/15. 

Reflectance accessories are available on modern UV-vis spectrometers and many are available which allow for variation of the incident angle for separation of specular reflectance and diffuse reflectance. Reflectance UV-vis has found applicahon in spectroelectrochemistry of thin films, polymer modified electrodes, and surface adsorbates such as self-assembled mono- and multilayers. A number of cell designs have been apphed and these are generally designed to fit into commercial reflectance attachments. A thin film reflectance cell is shown in Figure 14.8 (34). The electrode was fabricated by anodizahon of a thin layer... 

As with spectrophotometry, there are various accessories to the FTIR to allow for different experiments. Schematic representations of some of these accessories to measure specular reflectance are shown in Fig. 2.11. This modality of FTIR experiments are useful to measure thin films on reflective flat substrates, and bulk flat reflective materials. For very thin films shallower angles are recommended, as the optical path through the film will be longer. 

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